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Subtracting complex numbers

Learn how to break down the process of subtracting complex numbers into simple steps. Distribute the negative sign to get rid of parentheses, then add up the real and imaginary parts separately. Voila! You've got your answer in the form of a + bi. Created by Sal Khan and Monterey Institute for Technology and Education.

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Video transcript

We're asked to subtract. And we have the complex number 2 minus 3i. And from that, we are subtracting 6 minus 18i. So the first thing I'd like to do here is to just get rid of these parentheses. So we just have a bunch of real parts and imaginary parts that we can then add up together. So we have 2 minus 3i. And then we're subtracting this entire quantity. And to get rid of the parentheses, we can just distribute the negative sign. Or another way to think about it, we can say that this is negative 1 times all of this. So we can just distribute the negative sign. And negative 1 times 6 is negative 6. Let me do these in magenta. So this is negative 6. And then negative 1 times negative 18i-- well, that's just going to be positive 18i. Negative times a negative is a positive. And now we want to add the real parts, and we want to add the imaginary parts. So here's a real part here, 2. And then we have a minus 6. So we have 2 minus 6. And we want to add the imaginary parts. We have a negative. Let me do that in a different color. We have a negative 3i right over here. So negative 3i, or minus 3i right over there. And then we have a plus 18i or positive 18i. If you add the real parts, 2 minus 6 is negative 4. And you add the imaginary parts. If I have negative 3 of something and to that I add 18 of something, well, that's just going to leave me with 15 of that something. Or another way you could think about it, if I have 18 of something and I subtract 3 of that something, I'll have 15 of that something. And in this case, the something is i, is the imaginary unit. So this is going to be plus 15i. And we are done.